Question

ALLEMAAL Refer to the figure to find the following measure. If _C= 25° and mÃE = 100°, then moB 12.5° 50° 75°

Answer 1

The measure of an exterior angle is equal to half the difference of the measure of intercepted arcs. For the given extrior angle:

$m\angle C=\frac{1}{2}(\text{mAE}-mDB)$

Use the equation above to solve mDB:

$\begin{gathered} 25=\frac{1}{2}(100-mDB) \\ \\ (2)25=(100-mDB) \\ \\ 50=100-mDB \\ \\ 50-100=-mDB \\ \\ -50=-mDB \\ \\ -50(-1)=mDB \\ \\ \text{mDB}=50 \end{gathered}$

Then, the measure of arc DB is 50°